A unifrom disc of radius `R`, is resting on a table on its rim. The coefficient of friction between disc and table is `mu` Fig. Now the disc is pulled with a force `F` as shown in the Fig. What is the maximum value of `F` for which the disc rolls without slipping ?

Options

A. `mu`Mg
B. `2mu`Mg
C. `3mu`Mg
D. `4mu`Mg

Answer

c

Explanation

Let a be the acceleration of the center of the mass of disc. Then `Ma=F-f`………(i)
If there is no slipping, angular acceleration of the disc,
`alpha=a/R`
Now torque of the disc `tau=Ialpha = Rf`
or `tau=(1/2 MR^(2))alpha=Rf` `therefore` For a disc `I=1/2MR^(2)`
`therefore (1/2MR^(2))(a/R)=Rf rArr Ma=2f` (using (ii))
Substituting this in Eq. (i), we get
2f=F-f or `f=F/3`
Since, there is no slipping,
`therefore flemuMg rArr Fle3muMg therefore F_("max")= 3muMg`